{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Ornstein-Uhlenbeck process without parameter estimation\n",
    "\n",
    "The Ornstein-Uhlenbeck (OU) process is a continuous-time continuous-space\n",
    "stochastic process governed by the stochastic differential equation (SDE)\n",
    "\n",
    "          dY(t) = (Θ_1 - Θ_2 Y(t)) dt + Θ_3 dW(t)\n",
    "\n",
    "where W(t) is the Wiener process (standard Brownian motion). This OU process is\n",
    "stationary, Gaussian and Markovian. It is mean-reverting in the sense that it\n",
    "drifts towards its long-term mean of Θ_1 / Θ_2.\n",
    "\n",
    "For a step size Δt, the transition distribution can be obtained analytically as\n",
    "a Normal with mean μ(Δt) and variance σ^2(Δt):\n",
    "\n",
    "      Y(t + Δt) | Y(t) ~ Normal(μ(Δt), σ^2(Δt))\n",
    "                 μ(Δt) = Θ_1 / Θ_2 + (Y(t) - Θ_1 / Θ_2) exp(- Θ_2 Δt)\n",
    "               σ^2(Δt) = Θ_3^2 / (2 * Θ_2) * (1 - exp(- 2 Θ_2 Δt))\n",
    "\n",
    "Given a sequence of noisy observations of the process Y(t_n) ≈ y_n for\n",
    "1 <= n <= N, the task is to infer the posterior distribution over each Y(t_n).\n",
    "This choice is for the sake of simplicity, the example can be modified to\n",
    "infer posterior distributions over any Y(t).\n",
    "\n",
    "This example has been inspired by the LibBi example at\n",
    "http://libbi.org/packages/OrnsteinUhlenbeckBridge.html.\n",
    "\n",
    "##### References:\n",
    "- Y. Aït-Sahalia. Transition densities for interest rate and other nonlinear\n",
    "  diffusions. The Journal of Finance, 54(4):1361–1395, 1999. ISSN 1540-6261.\n",
    "  doi: 10.1111/0022-1082.00149.\n",
    "- L. Sun, C. Lee, and J. A. Hoeting. Penalized importance sampling for parameter\n",
    "  estimation in stochastic differential equations. 2013.\n",
    "  URL http://arxiv.org/abs/1305.4390.\n",
    "- Del Moral, Pierre, and Lawrence M. Murray. \"Sequential Monte Carlo with highly\n",
    "  informative observations.\" SIAM/ASA Journal on Uncertainty Quantification 3,\n",
    "  no. 1 (2015): 969-997. http://arxiv.org/pdf/1405.4081v2.pdf\n",
    "- C. E. Rasmussen and C. K. I. Williams. Gaussian Processes for Machine Learning\n",
    "  (Adaptive Computation and Machine Learning). The MIT Press, 2005.\n",
    "  ISBN 978-0-262-18253-9. URL http://www.gaussianprocess.org/gpml/."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True posterior of last state: Distributions.Normal(μ=0.04290846886466264, σ=0.009025242808127828)\n"
     ]
    },
    {
     "data": {
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       "A.undrag=function(){for(var b=r.length;b--;)r[b].el==this&&(this.unmousedown(r[b].start),r.splice(b,1),k.unbind(\"snap.drag.*.\"+this.id));!r.length&&a.unmousemove(e).unmouseup(l);return this}});C.plugin(function(a,v,y,C){y=y.prototype;var A=/^\\s*url\\((.+)\\)/,w=String,z=a._.$;a.filter={};y.filter=function(d){var f=this;\"svg\"!=f.type&&(f=f.paper);d=a.parse(w(d));var k=a._.id(),u=z(\"filter\");z(u,{id:k,filterUnits:\"userSpaceOnUse\"});u.appendChild(d.node);f.defs.appendChild(u);return new v(u)};k.on(\"snap.util.getattr.filter\",\n",
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       "amount2:1-d})};a.filter.invert.toString=function(){return this()};a.filter.brightness=function(d){null==d&&(d=1);return a.format('<feComponentTransfer><feFuncR type=\"linear\" slope=\"{amount}\"/><feFuncG type=\"linear\" slope=\"{amount}\"/><feFuncB type=\"linear\" slope=\"{amount}\"/></feComponentTransfer>',{amount:d})};a.filter.brightness.toString=function(){return this()};a.filter.contrast=function(d){null==d&&(d=1);return a.format('<feComponentTransfer><feFuncR type=\"linear\" slope=\"{amount}\" intercept=\"{amount2}\"/><feFuncG type=\"linear\" slope=\"{amount}\" intercept=\"{amount2}\"/><feFuncB type=\"linear\" slope=\"{amount}\" intercept=\"{amount2}\"/></feComponentTransfer>',\n",
       "{amount:d,amount2:0.5-d/2})};a.filter.contrast.toString=function(){return this()}});return C});\n",
       "\n",
       "]]> </script>\n",
       "<script> <![CDATA[\n",
       "\n",
       "(function (glob, factory) {\n",
       "    // AMD support\n",
       "    if (typeof define === \"function\" && define.amd) {\n",
       "        // Define as an anonymous module\n",
       "        define(\"Gadfly\", [\"Snap.svg\"], function (Snap) {\n",
       "            return factory(Snap);\n",
       "        });\n",
       "    } else {\n",
       "        // Browser globals (glob is window)\n",
       "        // Snap adds itself to window\n",
       "        glob.Gadfly = factory(glob.Snap);\n",
       "    }\n",
       "}(this, function (Snap) {\n",
       "\n",
       "var Gadfly = {};\n",
       "\n",
       "// Get an x/y coordinate value in pixels\n",
       "var xPX = function(fig, x) {\n",
       "    var client_box = fig.node.getBoundingClientRect();\n",
       "    return x * fig.node.viewBox.baseVal.width / client_box.width;\n",
       "};\n",
       "\n",
       "var yPX = function(fig, y) {\n",
       "    var client_box = fig.node.getBoundingClientRect();\n",
       "    return y * fig.node.viewBox.baseVal.height / client_box.height;\n",
       "};\n",
       "\n",
       "\n",
       "Snap.plugin(function (Snap, Element, Paper, global) {\n",
       "    // Traverse upwards from a snap element to find and return the first\n",
       "    // note with the \"plotroot\" class.\n",
       "    Element.prototype.plotroot = function () {\n",
       "        var element = this;\n",
       "        while (!element.hasClass(\"plotroot\") && element.parent() != null) {\n",
       "            element = element.parent();\n",
       "        }\n",
       "        return element;\n",
       "    };\n",
       "\n",
       "    Element.prototype.svgroot = function () {\n",
       "        var element = this;\n",
       "        while (element.node.nodeName != \"svg\" && element.parent() != null) {\n",
       "            element = element.parent();\n",
       "        }\n",
       "        return element;\n",
       "    };\n",
       "\n",
       "    Element.prototype.plotbounds = function () {\n",
       "        var root = this.plotroot()\n",
       "        var bbox = root.select(\".guide.background\").node.getBBox();\n",
       "        return {\n",
       "            x0: bbox.x,\n",
       "            x1: bbox.x + bbox.width,\n",
       "            y0: bbox.y,\n",
       "            y1: bbox.y + bbox.height\n",
       "        };\n",
       "    };\n",
       "\n",
       "    Element.prototype.plotcenter = function () {\n",
       "        var root = this.plotroot()\n",
       "        var bbox = root.select(\".guide.background\").node.getBBox();\n",
       "        return {\n",
       "            x: bbox.x + bbox.width / 2,\n",
       "            y: bbox.y + bbox.height / 2\n",
       "        };\n",
       "    };\n",
       "\n",
       "    // Emulate IE style mouseenter/mouseleave events, since Microsoft always\n",
       "    // does everything right.\n",
       "    // See: http://www.dynamic-tools.net/toolbox/isMouseLeaveOrEnter/\n",
       "    var events = [\"mouseenter\", \"mouseleave\"];\n",
       "\n",
       "    for (i in events) {\n",
       "        (function (event_name) {\n",
       "            var event_name = events[i];\n",
       "            Element.prototype[event_name] = function (fn, scope) {\n",
       "                if (Snap.is(fn, \"function\")) {\n",
       "                    var fn2 = function (event) {\n",
       "                        if (event.type != \"mouseover\" && event.type != \"mouseout\") {\n",
       "                            return;\n",
       "                        }\n",
       "\n",
       "                        var reltg = event.relatedTarget ? event.relatedTarget :\n",
       "                            event.type == \"mouseout\" ? event.toElement : event.fromElement;\n",
       "                        while (reltg && reltg != this.node) reltg = reltg.parentNode;\n",
       "\n",
       "                        if (reltg != this.node) {\n",
       "                            return fn.apply(this, event);\n",
       "                        }\n",
       "                    };\n",
       "\n",
       "                    if (event_name == \"mouseenter\") {\n",
       "                        this.mouseover(fn2, scope);\n",
       "                    } else {\n",
       "                        this.mouseout(fn2, scope);\n",
       "                    }\n",
       "                }\n",
       "                return this;\n",
       "            };\n",
       "        })(events[i]);\n",
       "    }\n",
       "\n",
       "\n",
       "    Element.prototype.mousewheel = function (fn, scope) {\n",
       "        if (Snap.is(fn, \"function\")) {\n",
       "            var el = this;\n",
       "            var fn2 = function (event) {\n",
       "                fn.apply(el, [event]);\n",
       "            };\n",
       "        }\n",
       "\n",
       "        this.node.addEventListener(\n",
       "            /Firefox/i.test(navigator.userAgent) ? \"DOMMouseScroll\" : \"mousewheel\",\n",
       "            fn2);\n",
       "\n",
       "        return this;\n",
       "    };\n",
       "\n",
       "\n",
       "    // Snap's attr function can be too slow for things like panning/zooming.\n",
       "    // This is a function to directly update element attributes without going\n",
       "    // through eve.\n",
       "    Element.prototype.attribute = function(key, val) {\n",
       "        if (val === undefined) {\n",
       "            return this.node.getAttribute(key);\n",
       "        } else {\n",
       "            this.node.setAttribute(key, val);\n",
       "            return this;\n",
       "        }\n",
       "    };\n",
       "\n",
       "    Element.prototype.init_gadfly = function() {\n",
       "        this.mouseenter(Gadfly.plot_mouseover)\n",
       "            .mouseleave(Gadfly.plot_mouseout)\n",
       "            .dblclick(Gadfly.plot_dblclick)\n",
       "            .mousewheel(Gadfly.guide_background_scroll)\n",
       "            .drag(Gadfly.guide_background_drag_onmove,\n",
       "                  Gadfly.guide_background_drag_onstart,\n",
       "                  Gadfly.guide_background_drag_onend);\n",
       "        this.mouseenter(function (event) {\n",
       "            init_pan_zoom(this.plotroot());\n",
       "        });\n",
       "        return this;\n",
       "    };\n",
       "});\n",
       "\n",
       "\n",
       "// When the plot is moused over, emphasize the grid lines.\n",
       "Gadfly.plot_mouseover = function(event) {\n",
       "    var root = this.plotroot();\n",
       "\n",
       "    var keyboard_zoom = function(event) {\n",
       "        if (event.which == 187) { // plus\n",
       "            increase_zoom_by_position(root, 0.1, true);\n",
       "        } else if (event.which == 189) { // minus\n",
       "            increase_zoom_by_position(root, -0.1, true);\n",
       "        }\n",
       "    };\n",
       "    root.data(\"keyboard_zoom\", keyboard_zoom);\n",
       "    window.addEventListener(\"keyup\", keyboard_zoom);\n",
       "\n",
       "    var xgridlines = root.select(\".xgridlines\"),\n",
       "        ygridlines = root.select(\".ygridlines\");\n",
       "\n",
       "    xgridlines.data(\"unfocused_strokedash\",\n",
       "                    xgridlines.attribute(\"stroke-dasharray\").replace(/(\\d)(,|$)/g, \"$1mm$2\"));\n",
       "    ygridlines.data(\"unfocused_strokedash\",\n",
       "                    ygridlines.attribute(\"stroke-dasharray\").replace(/(\\d)(,|$)/g, \"$1mm$2\"));\n",
       "\n",
       "    // emphasize grid lines\n",
       "    var destcolor = root.data(\"focused_xgrid_color\");\n",
       "    xgridlines.attribute(\"stroke-dasharray\", \"none\")\n",
       "              .selectAll(\"path\")\n",
       "              .animate({stroke: destcolor}, 250);\n",
       "\n",
       "    destcolor = root.data(\"focused_ygrid_color\");\n",
       "    ygridlines.attribute(\"stroke-dasharray\", \"none\")\n",
       "              .selectAll(\"path\")\n",
       "              .animate({stroke: destcolor}, 250);\n",
       "\n",
       "    // reveal zoom slider\n",
       "    root.select(\".zoomslider\")\n",
       "        .animate({opacity: 1.0}, 250);\n",
       "};\n",
       "\n",
       "// Reset pan and zoom on double click\n",
       "Gadfly.plot_dblclick = function(event) {\n",
       "  set_plot_pan_zoom(this.plotroot(), 0.0, 0.0, 1.0);\n",
       "};\n",
       "\n",
       "// Unemphasize grid lines on mouse out.\n",
       "Gadfly.plot_mouseout = function(event) {\n",
       "    var root = this.plotroot();\n",
       "\n",
       "    window.removeEventListener(\"keyup\", root.data(\"keyboard_zoom\"));\n",
       "    root.data(\"keyboard_zoom\", undefined);\n",
       "\n",
       "    var xgridlines = root.select(\".xgridlines\"),\n",
       "        ygridlines = root.select(\".ygridlines\");\n",
       "\n",
       "    var destcolor = root.data(\"unfocused_xgrid_color\");\n",
       "\n",
       "    xgridlines.attribute(\"stroke-dasharray\", xgridlines.data(\"unfocused_strokedash\"))\n",
       "              .selectAll(\"path\")\n",
       "              .animate({stroke: destcolor}, 250);\n",
       "\n",
       "    destcolor = root.data(\"unfocused_ygrid_color\");\n",
       "    ygridlines.attribute(\"stroke-dasharray\", ygridlines.data(\"unfocused_strokedash\"))\n",
       "              .selectAll(\"path\")\n",
       "              .animate({stroke: destcolor}, 250);\n",
       "\n",
       "    // hide zoom slider\n",
       "    root.select(\".zoomslider\")\n",
       "        .animate({opacity: 0.0}, 250);\n",
       "};\n",
       "\n",
       "\n",
       "var set_geometry_transform = function(root, tx, ty, scale) {\n",
       "    var xscalable = root.hasClass(\"xscalable\"),\n",
       "        yscalable = root.hasClass(\"yscalable\");\n",
       "\n",
       "    var old_scale = root.data(\"scale\");\n",
       "\n",
       "    var xscale = xscalable ? scale : 1.0,\n",
       "        yscale = yscalable ? scale : 1.0;\n",
       "\n",
       "    tx = xscalable ? tx : 0.0;\n",
       "    ty = yscalable ? ty : 0.0;\n",
       "\n",
       "    var t = new Snap.Matrix().translate(tx, ty).scale(xscale, yscale);\n",
       "\n",
       "    root.selectAll(\".geometry, image\")\n",
       "        .forEach(function (element, i) {\n",
       "            element.transform(t);\n",
       "        });\n",
       "\n",
       "    bounds = root.plotbounds();\n",
       "\n",
       "    if (yscalable) {\n",
       "        var xfixed_t = new Snap.Matrix().translate(0, ty).scale(1.0, yscale);\n",
       "        root.selectAll(\".xfixed\")\n",
       "            .forEach(function (element, i) {\n",
       "                element.transform(xfixed_t);\n",
       "            });\n",
       "\n",
       "        root.select(\".ylabels\")\n",
       "            .transform(xfixed_t)\n",
       "            .selectAll(\"text\")\n",
       "            .forEach(function (element, i) {\n",
       "                if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
       "                    var cx = element.asPX(\"x\"),\n",
       "                        cy = element.asPX(\"y\");\n",
       "                    var st = element.data(\"static_transform\");\n",
       "                    unscale_t = new Snap.Matrix();\n",
       "                    unscale_t.scale(1, 1/scale, cx, cy).add(st);\n",
       "                    element.transform(unscale_t);\n",
       "\n",
       "                    var y = cy * scale + ty;\n",
       "                    element.attr(\"visibility\",\n",
       "                        bounds.y0 <= y && y <= bounds.y1 ? \"visible\" : \"hidden\");\n",
       "                }\n",
       "            });\n",
       "    }\n",
       "\n",
       "    if (xscalable) {\n",
       "        var yfixed_t = new Snap.Matrix().translate(tx, 0).scale(xscale, 1.0);\n",
       "        var xtrans = new Snap.Matrix().translate(tx, 0);\n",
       "        root.selectAll(\".yfixed\")\n",
       "            .forEach(function (element, i) {\n",
       "                element.transform(yfixed_t);\n",
       "            });\n",
       "\n",
       "        root.select(\".xlabels\")\n",
       "            .transform(yfixed_t)\n",
       "            .selectAll(\"text\")\n",
       "            .forEach(function (element, i) {\n",
       "                if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
       "                    var cx = element.asPX(\"x\"),\n",
       "                        cy = element.asPX(\"y\");\n",
       "                    var st = element.data(\"static_transform\");\n",
       "                    unscale_t = new Snap.Matrix();\n",
       "                    unscale_t.scale(1/scale, 1, cx, cy).add(st);\n",
       "\n",
       "                    element.transform(unscale_t);\n",
       "\n",
       "                    var x = cx * scale + tx;\n",
       "                    element.attr(\"visibility\",\n",
       "                        bounds.x0 <= x && x <= bounds.x1 ? \"visible\" : \"hidden\");\n",
       "                    }\n",
       "            });\n",
       "    }\n",
       "\n",
       "    // we must unscale anything that is scale invariance: widths, raiduses, etc.\n",
       "    var size_attribs = [\"font-size\"];\n",
       "    var unscaled_selection = \".geometry, .geometry *\";\n",
       "    if (xscalable) {\n",
       "        size_attribs.push(\"rx\");\n",
       "        unscaled_selection += \", .xgridlines\";\n",
       "    }\n",
       "    if (yscalable) {\n",
       "        size_attribs.push(\"ry\");\n",
       "        unscaled_selection += \", .ygridlines\";\n",
       "    }\n",
       "\n",
       "    root.selectAll(unscaled_selection)\n",
       "        .forEach(function (element, i) {\n",
       "            // circle need special help\n",
       "            if (element.node.nodeName == \"circle\") {\n",
       "                var cx = element.attribute(\"cx\"),\n",
       "                    cy = element.attribute(\"cy\");\n",
       "                unscale_t = new Snap.Matrix().scale(1/xscale, 1/yscale,\n",
       "                                                        cx, cy);\n",
       "                element.transform(unscale_t);\n",
       "                return;\n",
       "            }\n",
       "\n",
       "            for (i in size_attribs) {\n",
       "                var key = size_attribs[i];\n",
       "                var val = parseFloat(element.attribute(key));\n",
       "                if (val !== undefined && val != 0 && !isNaN(val)) {\n",
       "                    element.attribute(key, val * old_scale / scale);\n",
       "                }\n",
       "            }\n",
       "        });\n",
       "};\n",
       "\n",
       "\n",
       "// Find the most appropriate tick scale and update label visibility.\n",
       "var update_tickscale = function(root, scale, axis) {\n",
       "    if (!root.hasClass(axis + \"scalable\")) return;\n",
       "\n",
       "    var tickscales = root.data(axis + \"tickscales\");\n",
       "    var best_tickscale = 1.0;\n",
       "    var best_tickscale_dist = Infinity;\n",
       "    for (tickscale in tickscales) {\n",
       "        var dist = Math.abs(Math.log(tickscale) - Math.log(scale));\n",
       "        if (dist < best_tickscale_dist) {\n",
       "            best_tickscale_dist = dist;\n",
       "            best_tickscale = tickscale;\n",
       "        }\n",
       "    }\n",
       "\n",
       "    if (best_tickscale != root.data(axis + \"tickscale\")) {\n",
       "        root.data(axis + \"tickscale\", best_tickscale);\n",
       "        var mark_inscale_gridlines = function (element, i) {\n",
       "            var inscale = element.attr(\"gadfly:scale\") == best_tickscale;\n",
       "            element.attribute(\"gadfly:inscale\", inscale);\n",
       "            element.attr(\"visibility\", inscale ? \"visible\" : \"hidden\");\n",
       "        };\n",
       "\n",
       "        var mark_inscale_labels = function (element, i) {\n",
       "            var inscale = element.attr(\"gadfly:scale\") == best_tickscale;\n",
       "            element.attribute(\"gadfly:inscale\", inscale);\n",
       "            element.attr(\"visibility\", inscale ? \"visible\" : \"hidden\");\n",
       "        };\n",
       "\n",
       "        root.select(\".\" + axis + \"gridlines\").selectAll(\"path\").forEach(mark_inscale_gridlines);\n",
       "        root.select(\".\" + axis + \"labels\").selectAll(\"text\").forEach(mark_inscale_labels);\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "var set_plot_pan_zoom = function(root, tx, ty, scale) {\n",
       "    var old_scale = root.data(\"scale\");\n",
       "    var bounds = root.plotbounds();\n",
       "\n",
       "    var width = bounds.x1 - bounds.x0,\n",
       "        height = bounds.y1 - bounds.y0;\n",
       "\n",
       "    // compute the viewport derived from tx, ty, and scale\n",
       "    var x_min = -width * scale - (scale * width - width),\n",
       "        x_max = width * scale,\n",
       "        y_min = -height * scale - (scale * height - height),\n",
       "        y_max = height * scale;\n",
       "\n",
       "    var x0 = bounds.x0 - scale * bounds.x0,\n",
       "        y0 = bounds.y0 - scale * bounds.y0;\n",
       "\n",
       "    var tx = Math.max(Math.min(tx - x0, x_max), x_min),\n",
       "        ty = Math.max(Math.min(ty - y0, y_max), y_min);\n",
       "\n",
       "    tx += x0;\n",
       "    ty += y0;\n",
       "\n",
       "    // when the scale change, we may need to alter which set of\n",
       "    // ticks is being displayed\n",
       "    if (scale != old_scale) {\n",
       "        update_tickscale(root, scale, \"x\");\n",
       "        update_tickscale(root, scale, \"y\");\n",
       "    }\n",
       "\n",
       "    set_geometry_transform(root, tx, ty, scale);\n",
       "\n",
       "    root.data(\"scale\", scale);\n",
       "    root.data(\"tx\", tx);\n",
       "    root.data(\"ty\", ty);\n",
       "};\n",
       "\n",
       "\n",
       "var scale_centered_translation = function(root, scale) {\n",
       "    var bounds = root.plotbounds();\n",
       "\n",
       "    var width = bounds.x1 - bounds.x0,\n",
       "        height = bounds.y1 - bounds.y0;\n",
       "\n",
       "    var tx0 = root.data(\"tx\"),\n",
       "        ty0 = root.data(\"ty\");\n",
       "\n",
       "    var scale0 = root.data(\"scale\");\n",
       "\n",
       "    // how off from center the current view is\n",
       "    var xoff = tx0 - (bounds.x0 * (1 - scale0) + (width * (1 - scale0)) / 2),\n",
       "        yoff = ty0 - (bounds.y0 * (1 - scale0) + (height * (1 - scale0)) / 2);\n",
       "\n",
       "    // rescale offsets\n",
       "    xoff = xoff * scale / scale0;\n",
       "    yoff = yoff * scale / scale0;\n",
       "\n",
       "    // adjust for the panel position being scaled\n",
       "    var x_edge_adjust = bounds.x0 * (1 - scale),\n",
       "        y_edge_adjust = bounds.y0 * (1 - scale);\n",
       "\n",
       "    return {\n",
       "        x: xoff + x_edge_adjust + (width - width * scale) / 2,\n",
       "        y: yoff + y_edge_adjust + (height - height * scale) / 2\n",
       "    };\n",
       "};\n",
       "\n",
       "\n",
       "// Initialize data for panning zooming if it isn't already.\n",
       "var init_pan_zoom = function(root) {\n",
       "    if (root.data(\"zoompan-ready\")) {\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    // The non-scaling-stroke trick. Rather than try to correct for the\n",
       "    // stroke-width when zooming, we force it to a fixed value.\n",
       "    var px_per_mm = root.node.getCTM().a;\n",
       "\n",
       "    // Drag events report deltas in pixels, which we'd like to convert to\n",
       "    // millimeters.\n",
       "    root.data(\"px_per_mm\", px_per_mm);\n",
       "\n",
       "    root.selectAll(\"path\")\n",
       "        .forEach(function (element, i) {\n",
       "        sw = element.asPX(\"stroke-width\") * px_per_mm;\n",
       "        if (sw > 0) {\n",
       "            element.attribute(\"stroke-width\", sw);\n",
       "            element.attribute(\"vector-effect\", \"non-scaling-stroke\");\n",
       "        }\n",
       "    });\n",
       "\n",
       "    // Store ticks labels original tranformation\n",
       "    root.selectAll(\".xlabels > text, .ylabels > text\")\n",
       "        .forEach(function (element, i) {\n",
       "            var lm = element.transform().localMatrix;\n",
       "            element.data(\"static_transform\",\n",
       "                new Snap.Matrix(lm.a, lm.b, lm.c, lm.d, lm.e, lm.f));\n",
       "        });\n",
       "\n",
       "    var xgridlines = root.select(\".xgridlines\");\n",
       "    var ygridlines = root.select(\".ygridlines\");\n",
       "    var xlabels = root.select(\".xlabels\");\n",
       "    var ylabels = root.select(\".ylabels\");\n",
       "\n",
       "    if (root.data(\"tx\") === undefined) root.data(\"tx\", 0);\n",
       "    if (root.data(\"ty\") === undefined) root.data(\"ty\", 0);\n",
       "    if (root.data(\"scale\") === undefined) root.data(\"scale\", 1.0);\n",
       "    if (root.data(\"xtickscales\") === undefined) {\n",
       "\n",
       "        // index all the tick scales that are listed\n",
       "        var xtickscales = {};\n",
       "        var ytickscales = {};\n",
       "        var add_x_tick_scales = function (element, i) {\n",
       "            xtickscales[element.attribute(\"gadfly:scale\")] = true;\n",
       "        };\n",
       "        var add_y_tick_scales = function (element, i) {\n",
       "            ytickscales[element.attribute(\"gadfly:scale\")] = true;\n",
       "        };\n",
       "\n",
       "        if (xgridlines) xgridlines.selectAll(\"path\").forEach(add_x_tick_scales);\n",
       "        if (ygridlines) ygridlines.selectAll(\"path\").forEach(add_y_tick_scales);\n",
       "        if (xlabels) xlabels.selectAll(\"text\").forEach(add_x_tick_scales);\n",
       "        if (ylabels) ylabels.selectAll(\"text\").forEach(add_y_tick_scales);\n",
       "\n",
       "        root.data(\"xtickscales\", xtickscales);\n",
       "        root.data(\"ytickscales\", ytickscales);\n",
       "        root.data(\"xtickscale\", 1.0);\n",
       "    }\n",
       "\n",
       "    var min_scale = 1.0, max_scale = 1.0;\n",
       "    for (scale in xtickscales) {\n",
       "        min_scale = Math.min(min_scale, scale);\n",
       "        max_scale = Math.max(max_scale, scale);\n",
       "    }\n",
       "    for (scale in ytickscales) {\n",
       "        min_scale = Math.min(min_scale, scale);\n",
       "        max_scale = Math.max(max_scale, scale);\n",
       "    }\n",
       "    root.data(\"min_scale\", min_scale);\n",
       "    root.data(\"max_scale\", max_scale);\n",
       "\n",
       "    // store the original positions of labels\n",
       "    if (xlabels) {\n",
       "        xlabels.selectAll(\"text\")\n",
       "               .forEach(function (element, i) {\n",
       "                   element.data(\"x\", element.asPX(\"x\"));\n",
       "               });\n",
       "    }\n",
       "\n",
       "    if (ylabels) {\n",
       "        ylabels.selectAll(\"text\")\n",
       "               .forEach(function (element, i) {\n",
       "                   element.data(\"y\", element.asPX(\"y\"));\n",
       "               });\n",
       "    }\n",
       "\n",
       "    // mark grid lines and ticks as in or out of scale.\n",
       "    var mark_inscale = function (element, i) {\n",
       "        element.attribute(\"gadfly:inscale\", element.attribute(\"gadfly:scale\") == 1.0);\n",
       "    };\n",
       "\n",
       "    if (xgridlines) xgridlines.selectAll(\"path\").forEach(mark_inscale);\n",
       "    if (ygridlines) ygridlines.selectAll(\"path\").forEach(mark_inscale);\n",
       "    if (xlabels) xlabels.selectAll(\"text\").forEach(mark_inscale);\n",
       "    if (ylabels) ylabels.selectAll(\"text\").forEach(mark_inscale);\n",
       "\n",
       "    // figure out the upper ond lower bounds on panning using the maximum\n",
       "    // and minum grid lines\n",
       "    var bounds = root.plotbounds();\n",
       "    var pan_bounds = {\n",
       "        x0: 0.0,\n",
       "        y0: 0.0,\n",
       "        x1: 0.0,\n",
       "        y1: 0.0\n",
       "    };\n",
       "\n",
       "    if (xgridlines) {\n",
       "        xgridlines\n",
       "            .selectAll(\"path\")\n",
       "            .forEach(function (element, i) {\n",
       "                if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
       "                    var bbox = element.node.getBBox();\n",
       "                    if (bounds.x1 - bbox.x < pan_bounds.x0) {\n",
       "                        pan_bounds.x0 = bounds.x1 - bbox.x;\n",
       "                    }\n",
       "                    if (bounds.x0 - bbox.x > pan_bounds.x1) {\n",
       "                        pan_bounds.x1 = bounds.x0 - bbox.x;\n",
       "                    }\n",
       "                    element.attr(\"visibility\", \"visible\");\n",
       "                }\n",
       "            });\n",
       "    }\n",
       "\n",
       "    if (ygridlines) {\n",
       "        ygridlines\n",
       "            .selectAll(\"path\")\n",
       "            .forEach(function (element, i) {\n",
       "                if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
       "                    var bbox = element.node.getBBox();\n",
       "                    if (bounds.y1 - bbox.y < pan_bounds.y0) {\n",
       "                        pan_bounds.y0 = bounds.y1 - bbox.y;\n",
       "                    }\n",
       "                    if (bounds.y0 - bbox.y > pan_bounds.y1) {\n",
       "                        pan_bounds.y1 = bounds.y0 - bbox.y;\n",
       "                    }\n",
       "                    element.attr(\"visibility\", \"visible\");\n",
       "                }\n",
       "            });\n",
       "    }\n",
       "\n",
       "    // nudge these values a little\n",
       "    pan_bounds.x0 -= 5;\n",
       "    pan_bounds.x1 += 5;\n",
       "    pan_bounds.y0 -= 5;\n",
       "    pan_bounds.y1 += 5;\n",
       "    root.data(\"pan_bounds\", pan_bounds);\n",
       "\n",
       "    root.data(\"zoompan-ready\", true)\n",
       "};\n",
       "\n",
       "\n",
       "// drag actions, i.e. zooming and panning\n",
       "var pan_action = {\n",
       "    start: function(root, x, y, event) {\n",
       "        root.data(\"dx\", 0);\n",
       "        root.data(\"dy\", 0);\n",
       "        root.data(\"tx0\", root.data(\"tx\"));\n",
       "        root.data(\"ty0\", root.data(\"ty\"));\n",
       "    },\n",
       "    update: function(root, dx, dy, x, y, event) {\n",
       "        var px_per_mm = root.data(\"px_per_mm\");\n",
       "        dx /= px_per_mm;\n",
       "        dy /= px_per_mm;\n",
       "\n",
       "        var tx0 = root.data(\"tx\"),\n",
       "            ty0 = root.data(\"ty\");\n",
       "\n",
       "        var dx0 = root.data(\"dx\"),\n",
       "            dy0 = root.data(\"dy\");\n",
       "\n",
       "        root.data(\"dx\", dx);\n",
       "        root.data(\"dy\", dy);\n",
       "\n",
       "        dx = dx - dx0;\n",
       "        dy = dy - dy0;\n",
       "\n",
       "        var tx = tx0 + dx,\n",
       "            ty = ty0 + dy;\n",
       "\n",
       "        set_plot_pan_zoom(root, tx, ty, root.data(\"scale\"));\n",
       "    },\n",
       "    end: function(root, event) {\n",
       "\n",
       "    },\n",
       "    cancel: function(root) {\n",
       "        set_plot_pan_zoom(root, root.data(\"tx0\"), root.data(\"ty0\"), root.data(\"scale\"));\n",
       "    }\n",
       "};\n",
       "\n",
       "var zoom_box;\n",
       "var zoom_action = {\n",
       "    start: function(root, x, y, event) {\n",
       "        var bounds = root.plotbounds();\n",
       "        var width = bounds.x1 - bounds.x0,\n",
       "            height = bounds.y1 - bounds.y0;\n",
       "        var ratio = width / height;\n",
       "        var xscalable = root.hasClass(\"xscalable\"),\n",
       "            yscalable = root.hasClass(\"yscalable\");\n",
       "        var px_per_mm = root.data(\"px_per_mm\");\n",
       "        x = xscalable ? x / px_per_mm : bounds.x0;\n",
       "        y = yscalable ? y / px_per_mm : bounds.y0;\n",
       "        var w = xscalable ? 0 : width;\n",
       "        var h = yscalable ? 0 : height;\n",
       "        zoom_box = root.rect(x, y, w, h).attr({\n",
       "            \"fill\": \"#000\",\n",
       "            \"opacity\": 0.25\n",
       "        });\n",
       "        zoom_box.data(\"ratio\", ratio);\n",
       "    },\n",
       "    update: function(root, dx, dy, x, y, event) {\n",
       "        var xscalable = root.hasClass(\"xscalable\"),\n",
       "            yscalable = root.hasClass(\"yscalable\");\n",
       "        var px_per_mm = root.data(\"px_per_mm\");\n",
       "        var bounds = root.plotbounds();\n",
       "        if (yscalable) {\n",
       "            y /= px_per_mm;\n",
       "            y = Math.max(bounds.y0, y);\n",
       "            y = Math.min(bounds.y1, y);\n",
       "        } else {\n",
       "            y = bounds.y1;\n",
       "        }\n",
       "        if (xscalable) {\n",
       "            x /= px_per_mm;\n",
       "            x = Math.max(bounds.x0, x);\n",
       "            x = Math.min(bounds.x1, x);\n",
       "        } else {\n",
       "            x = bounds.x1;\n",
       "        }\n",
       "\n",
       "        dx = x - zoom_box.attr(\"x\");\n",
       "        dy = y - zoom_box.attr(\"y\");\n",
       "        if (xscalable && yscalable) {\n",
       "            var ratio = zoom_box.data(\"ratio\");\n",
       "            var width = Math.min(Math.abs(dx), ratio * Math.abs(dy));\n",
       "            var height = Math.min(Math.abs(dy), Math.abs(dx) / ratio);\n",
       "            dx = width * dx / Math.abs(dx);\n",
       "            dy = height * dy / Math.abs(dy);\n",
       "        }\n",
       "        var xoffset = 0,\n",
       "            yoffset = 0;\n",
       "        if (dx < 0) {\n",
       "            xoffset = dx;\n",
       "            dx = -1 * dx;\n",
       "        }\n",
       "        if (dy < 0) {\n",
       "            yoffset = dy;\n",
       "            dy = -1 * dy;\n",
       "        }\n",
       "        if (isNaN(dy)) {\n",
       "            dy = 0.0;\n",
       "        }\n",
       "        if (isNaN(dx)) {\n",
       "            dx = 0.0;\n",
       "        }\n",
       "        zoom_box.transform(\"T\" + xoffset + \",\" + yoffset);\n",
       "        zoom_box.attr(\"width\", dx);\n",
       "        zoom_box.attr(\"height\", dy);\n",
       "    },\n",
       "    end: function(root, event) {\n",
       "        var xscalable = root.hasClass(\"xscalable\"),\n",
       "            yscalable = root.hasClass(\"yscalable\");\n",
       "        var zoom_bounds = zoom_box.getBBox();\n",
       "        if (zoom_bounds.width * zoom_bounds.height <= 0) {\n",
       "            return;\n",
       "        }\n",
       "        var plot_bounds = root.plotbounds();\n",
       "        var zoom_factor = 1.0;\n",
       "        if (yscalable) {\n",
       "            zoom_factor = (plot_bounds.y1 - plot_bounds.y0) / zoom_bounds.height;\n",
       "        } else {\n",
       "            zoom_factor = (plot_bounds.x1 - plot_bounds.x0) / zoom_bounds.width;\n",
       "        }\n",
       "        var tx = (root.data(\"tx\") - zoom_bounds.x) * zoom_factor + plot_bounds.x0,\n",
       "            ty = (root.data(\"ty\") - zoom_bounds.y) * zoom_factor + plot_bounds.y0;\n",
       "        set_plot_pan_zoom(root, tx, ty, root.data(\"scale\") * zoom_factor);\n",
       "        zoom_box.remove();\n",
       "    },\n",
       "    cancel: function(root) {\n",
       "        zoom_box.remove();\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.guide_background_drag_onstart = function(x, y, event) {\n",
       "    var root = this.plotroot();\n",
       "    var scalable = root.hasClass(\"xscalable\") || root.hasClass(\"yscalable\");\n",
       "    var zoomable = !event.altKey && !event.ctrlKey && event.shiftKey && scalable;\n",
       "    var panable = !event.altKey && !event.ctrlKey && !event.shiftKey && scalable;\n",
       "    var drag_action = zoomable ? zoom_action :\n",
       "                      panable  ? pan_action :\n",
       "                                 undefined;\n",
       "    root.data(\"drag_action\", drag_action);\n",
       "    if (drag_action) {\n",
       "        var cancel_drag_action = function(event) {\n",
       "            if (event.which == 27) { // esc key\n",
       "                drag_action.cancel(root);\n",
       "                root.data(\"drag_action\", undefined);\n",
       "            }\n",
       "        };\n",
       "        window.addEventListener(\"keyup\", cancel_drag_action);\n",
       "        root.data(\"cancel_drag_action\", cancel_drag_action);\n",
       "        drag_action.start(root, x, y, event);\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.guide_background_drag_onmove = function(dx, dy, x, y, event) {\n",
       "    var root = this.plotroot();\n",
       "    var drag_action = root.data(\"drag_action\");\n",
       "    if (drag_action) {\n",
       "        drag_action.update(root, dx, dy, x, y, event);\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.guide_background_drag_onend = function(event) {\n",
       "    var root = this.plotroot();\n",
       "    window.removeEventListener(\"keyup\", root.data(\"cancel_drag_action\"));\n",
       "    root.data(\"cancel_drag_action\", undefined);\n",
       "    var drag_action = root.data(\"drag_action\");\n",
       "    if (drag_action) {\n",
       "        drag_action.end(root, event);\n",
       "    }\n",
       "    root.data(\"drag_action\", undefined);\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.guide_background_scroll = function(event) {\n",
       "    if (event.shiftKey) {\n",
       "        increase_zoom_by_position(this.plotroot(), 0.001 * event.wheelDelta);\n",
       "        event.preventDefault();\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.zoomslider_button_mouseover = function(event) {\n",
       "    this.select(\".button_logo\")\n",
       "         .animate({fill: this.data(\"mouseover_color\")}, 100);\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.zoomslider_button_mouseout = function(event) {\n",
       "     this.select(\".button_logo\")\n",
       "         .animate({fill: this.data(\"mouseout_color\")}, 100);\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.zoomslider_zoomout_click = function(event) {\n",
       "    increase_zoom_by_position(this.plotroot(), -0.1, true);\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.zoomslider_zoomin_click = function(event) {\n",
       "    increase_zoom_by_position(this.plotroot(), 0.1, true);\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.zoomslider_track_click = function(event) {\n",
       "    // TODO\n",
       "};\n",
       "\n",
       "\n",
       "// Map slider position x to scale y using the function y = a*exp(b*x)+c.\n",
       "// The constants a, b, and c are solved using the constraint that the function\n",
       "// should go through the points (0; min_scale), (0.5; 1), and (1; max_scale).\n",
       "var scale_from_slider_position = function(position, min_scale, max_scale) {\n",
       "    var a = (1 - 2 * min_scale + min_scale * min_scale) / (min_scale + max_scale - 2),\n",
       "        b = 2 * Math.log((max_scale - 1) / (1 - min_scale)),\n",
       "        c = (min_scale * max_scale - 1) / (min_scale + max_scale - 2);\n",
       "    return a * Math.exp(b * position) + c;\n",
       "}\n",
       "\n",
       "// inverse of scale_from_slider_position\n",
       "var slider_position_from_scale = function(scale, min_scale, max_scale) {\n",
       "    var a = (1 - 2 * min_scale + min_scale * min_scale) / (min_scale + max_scale - 2),\n",
       "        b = 2 * Math.log((max_scale - 1) / (1 - min_scale)),\n",
       "        c = (min_scale * max_scale - 1) / (min_scale + max_scale - 2);\n",
       "    return 1 / b * Math.log((scale - c) / a);\n",
       "}\n",
       "\n",
       "var increase_zoom_by_position = function(root, delta_position, animate) {\n",
       "    var scale = root.data(\"scale\"),\n",
       "        min_scale = root.data(\"min_scale\"),\n",
       "        max_scale = root.data(\"max_scale\");\n",
       "    var position = slider_position_from_scale(scale, min_scale, max_scale);\n",
       "    position += delta_position;\n",
       "    scale = scale_from_slider_position(position, min_scale, max_scale);\n",
       "    set_zoom(root, scale, animate);\n",
       "}\n",
       "\n",
       "var set_zoom = function(root, scale, animate) {\n",
       "    var min_scale = root.data(\"min_scale\"),\n",
       "        max_scale = root.data(\"max_scale\"),\n",
       "        old_scale = root.data(\"scale\");\n",
       "    var new_scale = Math.max(min_scale, Math.min(scale, max_scale));\n",
       "    if (animate) {\n",
       "        Snap.animate(\n",
       "            old_scale,\n",
       "            new_scale,\n",
       "            function (new_scale) {\n",
       "                update_plot_scale(root, new_scale);\n",
       "            },\n",
       "            200);\n",
       "    } else {\n",
       "        update_plot_scale(root, new_scale);\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "var update_plot_scale = function(root, new_scale) {\n",
       "    var trans = scale_centered_translation(root, new_scale);\n",
       "    set_plot_pan_zoom(root, trans.x, trans.y, new_scale);\n",
       "\n",
       "    root.selectAll(\".zoomslider_thumb\")\n",
       "        .forEach(function (element, i) {\n",
       "            var min_pos = element.data(\"min_pos\"),\n",
       "                max_pos = element.data(\"max_pos\"),\n",
       "                min_scale = root.data(\"min_scale\"),\n",
       "                max_scale = root.data(\"max_scale\");\n",
       "            var xmid = (min_pos + max_pos) / 2;\n",
       "            var xpos = slider_position_from_scale(new_scale, min_scale, max_scale);\n",
       "            element.transform(new Snap.Matrix().translate(\n",
       "                Math.max(min_pos, Math.min(\n",
       "                         max_pos, min_pos + (max_pos - min_pos) * xpos)) - xmid, 0));\n",
       "    });\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.zoomslider_thumb_dragmove = function(dx, dy, x, y, event) {\n",
       "    var root = this.plotroot();\n",
       "    var min_pos = this.data(\"min_pos\"),\n",
       "        max_pos = this.data(\"max_pos\"),\n",
       "        min_scale = root.data(\"min_scale\"),\n",
       "        max_scale = root.data(\"max_scale\"),\n",
       "        old_scale = root.data(\"old_scale\");\n",
       "\n",
       "    var px_per_mm = root.data(\"px_per_mm\");\n",
       "    dx /= px_per_mm;\n",
       "    dy /= px_per_mm;\n",
       "\n",
       "    var xmid = (min_pos + max_pos) / 2;\n",
       "    var xpos = slider_position_from_scale(old_scale, min_scale, max_scale) +\n",
       "                   dx / (max_pos - min_pos);\n",
       "\n",
       "    // compute the new scale\n",
       "    var new_scale = scale_from_slider_position(xpos, min_scale, max_scale);\n",
       "    new_scale = Math.min(max_scale, Math.max(min_scale, new_scale));\n",
       "\n",
       "    update_plot_scale(root, new_scale);\n",
       "    event.stopPropagation();\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.zoomslider_thumb_dragstart = function(x, y, event) {\n",
       "    this.animate({fill: this.data(\"mouseover_color\")}, 100);\n",
       "    var root = this.plotroot();\n",
       "\n",
       "    // keep track of what the scale was when we started dragging\n",
       "    root.data(\"old_scale\", root.data(\"scale\"));\n",
       "    event.stopPropagation();\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.zoomslider_thumb_dragend = function(event) {\n",
       "    this.animate({fill: this.data(\"mouseout_color\")}, 100);\n",
       "    event.stopPropagation();\n",
       "};\n",
       "\n",
       "\n",
       "var toggle_color_class = function(root, color_class, ison) {\n",
       "    var guides = root.selectAll(\".guide.\" + color_class + \",.guide .\" + color_class);\n",
       "    var geoms = root.selectAll(\".geometry.\" + color_class + \",.geometry .\" + color_class);\n",
       "    if (ison) {\n",
       "        guides.animate({opacity: 0.5}, 250);\n",
       "        geoms.animate({opacity: 0.0}, 250);\n",
       "    } else {\n",
       "        guides.animate({opacity: 1.0}, 250);\n",
       "        geoms.animate({opacity: 1.0}, 250);\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.colorkey_swatch_click = function(event) {\n",
       "    var root = this.plotroot();\n",
       "    var color_class = this.data(\"color_class\");\n",
       "\n",
       "    if (event.shiftKey) {\n",
       "        root.selectAll(\".colorkey text\")\n",
       "            .forEach(function (element) {\n",
       "                var other_color_class = element.data(\"color_class\");\n",
       "                if (other_color_class != color_class) {\n",
       "                    toggle_color_class(root, other_color_class,\n",
       "                                       element.attr(\"opacity\") == 1.0);\n",
       "                }\n",
       "            });\n",
       "    } else {\n",
       "        toggle_color_class(root, color_class, this.attr(\"opacity\") == 1.0);\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "return Gadfly;\n",
       "\n",
       "}));\n",
       "\n",
       "\n",
       "//@ sourceURL=gadfly.js\n",
       "\n",
       "(function (glob, factory) {\n",
       "    // AMD support\n",
       "      if (typeof require === \"function\" && typeof define === \"function\" && define.amd) {\n",
       "        require([\"Snap.svg\", \"Gadfly\"], function (Snap, Gadfly) {\n",
       "            factory(Snap, Gadfly);\n",
       "        });\n",
       "      } else {\n",
       "          factory(glob.Snap, glob.Gadfly);\n",
       "      }\n",
       "})(window, function (Snap, Gadfly) {\n",
       "    var fig = Snap(\"#img-1c80b346\");\n",
       "fig.select(\"#img-1c80b346-5\")\n",
       "   .init_gadfly();\n",
       "fig.select(\"#img-1c80b346-7\")\n",
       "   .plotroot().data(\"unfocused_ygrid_color\", \"#D0D0E0\")\n",
       ";\n",
       "fig.select(\"#img-1c80b346-7\")\n",
       "   .plotroot().data(\"focused_ygrid_color\", \"#A0A0A0\")\n",
       ";\n",
       "fig.select(\"#img-1c80b346-8\")\n",
       "   .plotroot().data(\"unfocused_xgrid_color\", \"#D0D0E0\")\n",
       ";\n",
       "fig.select(\"#img-1c80b346-8\")\n",
       "   .plotroot().data(\"focused_xgrid_color\", \"#A0A0A0\")\n",
       ";\n",
       "fig.select(\"#img-1c80b346-14\")\n",
       "   .data(\"mouseover_color\", \"#CD5C5C\")\n",
       ";\n",
       "fig.select(\"#img-1c80b346-14\")\n",
       "   .data(\"mouseout_color\", \"#6A6A6A\")\n",
       ";\n",
       "fig.select(\"#img-1c80b346-14\")\n",
       "   .click(Gadfly.zoomslider_zoomin_click)\n",
       ".mouseenter(Gadfly.zoomslider_button_mouseover)\n",
       ".mouseleave(Gadfly.zoomslider_button_mouseout)\n",
       ";\n",
       "fig.select(\"#img-1c80b346-16\")\n",
       "   .data(\"max_pos\", 120.42)\n",
       ";\n",
       "fig.select(\"#img-1c80b346-16\")\n",
       "   .data(\"min_pos\", 103.42)\n",
       ";\n",
       "fig.select(\"#img-1c80b346-16\")\n",
       "   .click(Gadfly.zoomslider_track_click);\n",
       "fig.select(\"#img-1c80b346-17\")\n",
       "   .data(\"max_pos\", 120.42)\n",
       ";\n",
       "fig.select(\"#img-1c80b346-17\")\n",
       "   .data(\"min_pos\", 103.42)\n",
       ";\n",
       "fig.select(\"#img-1c80b346-17\")\n",
       "   .data(\"mouseover_color\", \"#CD5C5C\")\n",
       ";\n",
       "fig.select(\"#img-1c80b346-17\")\n",
       "   .data(\"mouseout_color\", \"#6A6A6A\")\n",
       ";\n",
       "fig.select(\"#img-1c80b346-17\")\n",
       "   .drag(Gadfly.zoomslider_thumb_dragmove,\n",
       "     Gadfly.zoomslider_thumb_dragstart,\n",
       "     Gadfly.zoomslider_thumb_dragend)\n",
       ";\n",
       "fig.select(\"#img-1c80b346-18\")\n",
       "   .data(\"mouseover_color\", \"#CD5C5C\")\n",
       ";\n",
       "fig.select(\"#img-1c80b346-18\")\n",
       "   .data(\"mouseout_color\", \"#6A6A6A\")\n",
       ";\n",
       "fig.select(\"#img-1c80b346-18\")\n",
       "   .click(Gadfly.zoomslider_zoomout_click)\n",
       ".mouseenter(Gadfly.zoomslider_button_mouseover)\n",
       ".mouseleave(Gadfly.zoomslider_button_mouseout)\n",
       ";\n",
       "    });\n",
       "]]> </script>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "Plot(...)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Turing, Distributions\n",
    "\n",
    "#= The parameter values of Θ_1, Θ_2, Θ_3 follow [Aït-Sahalia, 1999],\n",
    "   [Sun et al., 2013] and [Del Moral et al., 2015]. =#\n",
    "const Θ_1 = 0.0187\n",
    "const Θ_2 = 0.2610\n",
    "const Θ_3 = 0.0224\n",
    "\n",
    "#= [Del Moral, 2015] observe the OU process directly with no observation noise,\n",
    "and their task is to simulate the diffusion bridges between the observed values.\n",
    "Our examples uses observation noise with standard deviation σ_y > 0, as this is\n",
    "required for inference to work at this stage. =#\n",
    "const σ_y = 0.01\n",
    "\n",
    "#= The observation times ts and the corresponding observed values.\n",
    "   It is assumed that the observation times are sorted increasingly. =#\n",
    "ts      = [0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0]\n",
    "data_ys = [0.0, -0.009114765844660457, 0.029830170268001097,\n",
    "0.021755657377028295, 0.013934983652697013, 0.01910503829939146,\n",
    "0.049404191951179434, 0.03253467537333853, 0.07701445971172535,\n",
    "0.04618793002053633, 0.04001971135990065]\n",
    "N = length(ts)\n",
    "\n",
    "# The transition distribution of the OU process\n",
    "function trans(Yt, Δt)\n",
    "  mean = Θ_1 / Θ_2 + (Yt - Θ_1 / Θ_2) * exp(- Θ_2 * Δt)\n",
    "  variance = Θ_3 * Θ_3 / (2 * Θ_2) * (1 - exp(- 2 * Θ_2 * Δt))\n",
    "  # Normal is initialized with mean and standard deviation, not variance!\n",
    "  return Normal(mean, sqrt(variance))\n",
    "end\n",
    "\n",
    "# The generative model of the OU process\n",
    "@model ou begin\n",
    "  # use TArray to support array copying when particles are duplicated!\n",
    "  Y = TArray(Float64, N)\n",
    "  Y[1] = 0.0\n",
    "  for n = 2:N\n",
    "    Δt = ts[n] - ts[n-1]\n",
    "    @assume(Y[n] ~ trans(Y[n-1], Δt))\n",
    "    @observe(data_ys[n] ~ Normal(Y[n], σ_y))\n",
    "  end\n",
    "  @predict Y\n",
    "end\n",
    "\n",
    "\n",
    "#= This concludes the example. The remainder of this script verifies that\n",
    "inference works properly by checking that (potentially weighted) samples from\n",
    "the posterior over Y[N] (the last element of the sequence Y) approximate the\n",
    "exact posterior over Y[N].\n",
    "\n",
    "The exact posterior over Y[N] is obtained by recalling that our OU process\n",
    "is a Gaussian process [Rasmussen and Williams, 2005] with constant mean function\n",
    "μ(t) = Θ_1 / Θ_2 and stationary covariance function\n",
    "\n",
    "          k(r) = Θ_3^2 / (2 * Θ_2) * exp(- Θ_2 * |r|)\n",
    "\n",
    "which is also known as the exponential, Laplace, or Laplacian kernel. (See\n",
    "Appendix B.2.1 in [Rasmussen and Williams, 2005] for a derivation.) Hence exact\n",
    "posteriors can be obtained by performing standard GP regression, which involves\n",
    "inverting a kernel matrix A := (K + σ_y^2 I). =#\n",
    "\n",
    "k(x, y) = Θ_3^2 / (2 * Θ_2) * exp(- Θ_2 * abs(x - y))\n",
    "K = [k(x1, x2)::Float64 for x1=ts, x2=ts]\n",
    "noise_matrix = σ_y^2 * eye(N)\n",
    "noise_matrix[1, 1] = 0.0 # observed 0.0 at time t=0 with no noise\n",
    "A = K + noise_matrix\n",
    "Ainv = inv(A)\n",
    "\n",
    "# Compute true posterior over Y[N], the value of Y(t) at time t=ts[N]\n",
    "x_star = ts[N]\n",
    "k_star = [k(x, x_star)::Float64 for x=ts]\n",
    "f_star_mean = transpose(k_star) * (A \\ (data_ys - Θ_1 / Θ_2)) + Θ_1 / Θ_2\n",
    "f_star_variance = k(x_star, x_star) - transpose(k_star) * (A \\ k_star)\n",
    "f_star_std = sqrt(f_star_variance)\n",
    "f_star_posterior = Normal(f_star_mean[1], f_star_std[1])\n",
    "println(\"True posterior of last state: \", f_star_posterior)\n",
    "\n",
    "# KL-divergence between a Normal MLE-fitted to samples and true posterior\n",
    "function ou_divergence(samples, weights)\n",
    "  fitted = fit_mle(Normal, samples, weights)\n",
    "  return Turing.kl(fitted, f_star_posterior)\n",
    "end\n",
    "function ou_divergence(samples :: Vector{Float64})\n",
    "  weights = fill(Float64(1), length(samples))\n",
    "  return ou_divergence(samples, weights)\n",
    "end\n",
    "\n",
    "#= Compute the KL-divergence between moment-matched Normal from samples and\n",
    "exact posterior, as the number of samples increases =#\n",
    "num_samples = [10, 30, 100, 300, 1000, 3000, 10000]\n",
    "samples = sample(ou, SMC(maximum(num_samples)))\n",
    "samples_lasty = [res[N]::Float64 for res=samples[:Y]]\n",
    "kl_divergences = map(n -> ou_divergence(samples_lasty[1:n]), num_samples)\n",
    "\n",
    "# Plot the results using Gadfly\n",
    "using Gadfly\n",
    "plot(x=num_samples, y=kl_divergences,\n",
    "     Scale.x_log10, Scale.y_log10,\n",
    "     Guide.title(\"KL-divergence between exact and moment matched posterior\"),\n",
    "     Guide.xlabel(\"number of samples\"), Guide.ylabel(\"KL-divergence\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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